Large Deviation Analysis for Quantum Security via Smoothing of Rényi Entropy of Order 2

It is known that the security evaluation can be done by smoothing of Rényi entropy of order 2 in the classical and quantum settings when we apply universal2 hash functions. Using the smoothing of Rényi entropy of order 2, we derive security bounds for L1 distinguishability and modified mutual information criterion under the classical and quantum setting, and have derived these exponential decreasing rates. These results are extended to the case when we apply ε-almost dual universal2 hash functions. Further, we apply this analysis to the secret key generation with error correction. Index Terms exponential rate, non-asymptotic setting, secret key generation, universal hash function, almost dual universal2 hash function